Question

given ( m parallel n ), find the value of ( x ).

Explanation:

Step1: Identify the relationship

Since \( m \parallel n \), the angle of \( 102^\circ \) and \( x^\circ \) are same - side interior angles (or supplementary angles as they lie on the same side of the transversal and between the two parallel lines). The sum of same - side interior angles is \( 180^\circ \). So we can write the equation \( 102 + x=180 \).

Step2: Solve for \( x \)

To find \( x \), we subtract \( 102 \) from both sides of the equation \( 102 + x = 180 \).
\( x=180 - 102 \)
\( x = 78 \)

Answer:

\( x = 78 \)